Proteins and their interactions play fundamental roles in all biological processes. Accurate description of protein structure and interactions is a fundamental step towards understanding biological life and highly relevant in the development of therapeutics and drugs. However, there is a large gap between the number of available protein sequences and the number of proteins (complexes) with solved structures and accurate interaction description, which has to be filled by computational prediction. The long-term goal of this project is to apply statistical machine learning and optimization algorithms to understand protein sequence-structure-function relationship by analyzing low- and high-throughput sequence, structure and functional data and to develop algorithms for structure and functional prediction. Our hypothesis is that by developing sophisticated algorithms to take advantage of the growing sequence and structure data, we can model sequence-structure relationship much more accurately and significantly improve structure and functional prediction, in particular for this proposal, residue (atomic) interaction strength prediction and remote homology detection. This project has produced a few CASP-winning, widely-used data-driven algorithms and web server (http://raptorx.uchicago.edu) for monomer protein modeling. This renewal will not only further develop machine learning algorithms (especially Deep Learning and probabilistic graphical models) for monomer proteins, but also branch out to protein interactions (complexes). The specific aims are: (1) develop novel structure learning algorithms to predict inter-reside contacts and coevolved residues; (2) develop context-specific, coevolution-based, and distance-dependent statistical potentials using a new machine learning model called Deep Conditional (Markov) Neural Fields (DeepCNF); (3) develop Markov Random Fields (MRF) and DeepCNF methods for remote protein (interface/complex) homology detection and fold recognition to make use of long-range residue interaction predicted by the first two aims. This renewal will lead to further understanding and new models of protein sequence-structure-function relationship and yield publicly available software and servers for automated, accurate, quantitative analysis for a wide range of proteins and their interactions. The impact will be multiplied by tens of thousands of worldwide users employing the resulting software/servers to study a wide variety of proteins and interactions relevant to basic biological research and human diseases, in both low- and high-throughput experiments.